Non-invasive imaging of solute redistribution below evaporating surfaces using 23Na-MRI

This study utilizes 23Na-MRI to experimentally demonstrate that density-driven fingering instabilities in high-permeability porous media cause significant downward redistribution of evaporating solutes, preventing surface saturation, whereas lower-permeability media allow for extreme near-surface concentration buildup.

The Gist

The Big Picture: Salt, Sand, and the "Heavy Rain" Effect

Imagine you have two cups of sand. One cup is filled with coarse, chunky gravel (let's call it the "Fast Sand"), and the other is filled with very fine, powdery dust (the "Slow Sand"). You pour salty water into both cups until they are completely soaked. Then, you leave them out in a warm, dry wind to let the water evaporate.

The question the researchers asked is: Where does the salt go as the water disappears?

Common sense might suggest the salt just piles up on the very top surface, like a crust forming on a puddle. However, this study used a special "magic camera" (MRI) to watch what actually happens inside the sand, and they found something surprising: It depends entirely on how big the holes in the sand are.

The Tools: The "Magic Camera"

To see inside the wet sand without digging it up, the scientists used a machine similar to a hospital MRI scanner. But instead of taking pictures of your knee, they tuned it to see Sodium (the "Na" in table salt).

Think of this as a camera that can see the salt glowing inside the wet sand. They could take 3D snapshots over time to watch the salt move, almost like watching a time-lapse video of a crowd moving through a room.

The Experiment: Two Different Stories

The researchers ran the experiment on two types of sand with very different "permeability" (how easily water can flow through them).

1. The "Slow Sand" (Fine Grains)

• What happened: As the water evaporated from the top, the salt had nowhere to go but up. It got stuck in the tiny, tight spaces near the surface.
• The Result: The salt piled up into a thick, concentrated layer right at the top, almost reaching the point where it would turn into solid rock (crystallize).
• The Analogy: Imagine a crowded hallway where people (water molecules) are trying to leave, but the doors are tiny. The people get stuck right at the exit, and the "salt" (a heavy backpack) piles up right there, making it very hard for anyone else to get out. The evaporation slowed down significantly because the salt was clogging the top.

2. The "Fast Sand" (Coarse Grains)

• What happened: At first, the salt tried to pile up at the top, just like in the slow sand. But because the holes in this sand were larger, something different happened. The salty water at the top became very heavy (dense).
• The Result: Gravity took over. The heavy, salty water couldn't stay at the top, so it sank down into the sand like a heavy stone dropping into a pool. It created a "plume" or a "finger" of salty water that moved downward, carrying the salt deep into the column.
• The Analogy: Imagine a crowd in a wide-open stadium. As people leave, a group of people carrying heavy backpacks (the salt) gets so heavy that they can't stay at the front. Instead, they slip past the crowd and sink to the back of the room. The top stays relatively clear, and the "salt" gets redistributed deep inside the sand.

Why This Matters (According to the Paper)

The study confirms a theory that scientists had only guessed at before: Salt doesn't always stay at the top.

• In tight sand: Salt stays at the surface, gets super concentrated, and slows down evaporation. This is bad for things like building materials (it causes weathering) or soil (it causes salinization).
• In loose sand: The salt sinks down. This means the surface stays less salty, evaporation keeps going at a steady pace, and the salt ends up deeper in the ground rather than forming a crust on top.

The "Finger" vs. The "Crust"

The researchers compared their real-world observations with computer simulations. The computer models predicted exactly what they saw in the MRI:

• The Slow Sand developed a "crust" of salt at the top.
• The Fast Sand developed "fingers" of salt that dripped downward.

They also checked the math using a concept called the "Rayleigh number" (a fancy way of measuring if a fluid is heavy enough to sink). The math predicted that the Fast Sand would be unstable and sink, while the Slow Sand would stay put. The MRI camera proved the math right.

Summary

This paper is like a detective story where scientists used a special camera to solve a mystery about salt and sand. They discovered that the size of the sand grains acts like a traffic controller:

• Small grains trap the salt at the door, creating a heavy traffic jam (crust).
• Large grains let the heavy salt sink to the basement, clearing the way for more water to evaporate.

This helps us understand how salt moves in nature, whether it's drying out a lake, damaging a building, or affecting soil in a garden.

Technical Summary

Technical Summary: Non-invasive imaging of solute redistribution below evaporating surfaces using 23Na-MRI

Problem Statement
Saline water evaporation from porous media is a critical process linked to soil salinization and building material weathering. While previous studies have identified stages of evaporation (SS1–SS3), the dynamics of solute accumulation near the surface remain complex. Recent theoretical models (e.g., Bringedal et al., 2022) suggest that in fully saturated, high-permeability porous media, evaporation can induce density-driven instabilities. As salt accumulates at the surface, the resulting increase in fluid density may trigger downward fingering flow, redistributing solutes away from the evaporative front. However, this phenomenon has primarily been observed theoretically or in two-dimensional Hele-Shaw cells. There is a lack of three-dimensional experimental evidence confirming whether density-driven downward flow occurs in natural porous media under wicking conditions, particularly regarding how intrinsic permeability influences the transition from surface enrichment to downward redistribution.

Methodology
To address this gap, the authors conducted evaporation experiments on two porous media samples with contrasting intrinsic permeabilities: F36 (medium sand, $k \approx 7.83 \times 10^{-12} \, \text{m}^2$) and W3 (very fine sand, $k \approx 3.2 \times 10^{-14} \, \text{m}^2$). Both samples were initially saturated with a 1.0 mol L⁻¹ NaCl solution and supplied with the same solution from a bottom reservoir to maintain saturation (wicking conditions) while evaporation was driven by a turbulent N₂ gas stream.

The core innovation of the study is the application of non-invasive ²³Na-MRI (Sodium-23 Magnetic Resonance Imaging) to monitor the spatiotemporal redistribution of NaCl.

• Imaging Protocols: The study utilized a 4.7 T Bruker scanner. Different pulse sequences (3D RARE for F36 and MSSE for W3) were employed to accommodate the faster T₂ relaxation times observed in the finer W3 pores.
• Calibration: Quantitative Na concentration maps were generated using calibration curves derived from samples with known NaCl concentrations (0 to 5 mol L⁻¹). A linear relationship was established for F36, while a second-order polynomial was required for W3 due to surface relaxation effects.
• Validation: ¹H-MRI was used concurrently to verify that samples remained fully saturated throughout the experiments. Mass balances were calculated by comparing MRI-derived Na masses against evaporative mass loss data.
• Numerical Modeling: Experimental results were compared against 2D numerical simulations using the DuMux simulator, which incorporates density-driven flow and was initialized with small random perturbations to trigger instabilities.

Key Results

1. Divergent Solute Behavior: The experiments revealed fundamentally different solute redistribution patterns based on permeability.

   • W3 (Low Permeability): Exhibited a gradual, shallow enrichment of Na near the surface. Concentrations in the top 1 mm reached approximately 6.7 mol L⁻¹ (approaching or exceeding the solubility limit of 6.14 mol L⁻¹). No downward fingering was observed. Consequently, the evaporation rate dropped sharply from ~9 mm d⁻¹ to ~4 mm d⁻¹ as surface concentration increased, reducing vapor pressure.
   • F36 (High Permeability): Showed an initial surface enrichment, but within the first hour, a density-driven downward plume (fingering) developed. This plume redistributed NaCl deeper into the column, preventing extreme surface accumulation. Surface concentrations remained moderate (peaking at 2.5 mol L⁻¹), and the evaporation rate remained relatively constant (6 mm d⁻¹) throughout the experiment.

2. Stability Analysis: The observed behavior aligns with stability criteria defined by Wooding et al. (1997a). The Rayleigh number ($R_\delta$) for F36 was calculated at 33.5 (indicating instability), whereas for W3, it was 0.59 (stable). Linear stability analysis by Bringedal et al. (2022) predicted an instability onset time of 0.61 hours for F36, which matched the experimental observation of fingering appearing at approximately 1 hour.

3. Model Comparison: Numerical simulations using DuMux showed qualitative agreement with experimental data. The model successfully reproduced the surface enrichment in W3 and the formation of downward fingers in F36. However, discrepancies existed in the late-stage concentration profiles, attributed to boundary effects (finite sample height) and simplified boundary conditions in the model.

Significance and Claims
The study provides the first experimental confirmation, on a three-dimensional scale, of density-driven solute redistribution in evaporating saturated porous media. The authors claim that their work validates theoretical predictions that intrinsic permeability is a decisive factor in whether evaporation leads to surface crust formation or deep solute redistribution.

Specifically, the paper asserts that:

• High-permeability media allow for density-driven downward flow that counteracts the upward evaporative flux, thereby delaying surface saturation and crust formation.
• Low-permeability media trap solutes near the surface, leading to rapid concentration increases, reduced evaporation rates, and earlier crust formation.
• ²³Na-MRI is a viable, non-invasive tool for quantifying solute redistribution in porous media, capable of resolving density-driven instabilities despite challenges with signal-to-noise ratios.

The authors conclude that these findings have implications for predicting evaporation rates, the timing of salt crust formation, and the hydrology of saline groundwater systems, such as those found in playas and salt flats. They modestly suggest that future work should explore different salt types and heterogeneous media, but the primary contribution remains the experimental verification of density-driven flow mechanisms previously only theorized.